It is well known that the propagation velocity of ultrasonic waves through a sample gas is presented by a function of the concentration and the temperature of the sample gas. The velocity C(m/sec) of ultrasonic waves propagating through a stationary gas is presented by flowing equation (1) with mean molecular weight M and the temperature T(K).C=(κRT/M)1/2  (1)Where:    κ: ratio of molecular specific heat at constant volume and molecular specific heat at constant pressure    R: gas constant
Therefore, measuring the velocity of ultrasonic waves C(m/sec) propagating through a sample gas and the temperature T(K) of the sample gas will provide the mean molecular weight M of the sample gas through a calculation. For example, the mean molecular weight M of a sample gas containing an oxygen-nitrogen gas mixture of a mixture ratio P:(1−P) (0≦P≦1) will be calculated by following equation (2).M=MO2P+MN2(1−P)  (2)Where:MO2: Molecular Weight of oxygen gasMN2: Molecular Weight of nitrogen gas
Therefore, the oxygen concentration P will be obtained through a calculation on the basis of the measurement of mean molecular weight M. When the sample gas is an oxygen-nitrogen mixture, κ=1.4 is reasonable over a wide range of the oxygen-nitrogen mixture ratio.
When the velocity of ultrasonic waves propagating through a sample gas is C(m/sec) and the flow velocity of the sample gas is V(m/sec), the velocity of ultrasonic waves C1(m/sec) propagating in the forward direction relative to the sample gas flow is C1=C+V, and the velocity of ultrasonic waves C2(m/sec) propagating in the backward direction relative to the sample gas flow is C2=C−V. Therefore, the velocity of the sample gas flow V(m/sec) is calculated by following equation (3).V=(C1−C2)/2  (3)
The flow rate (m3/sec) of the sample gas will be obtained by multiplying the velocity of the sample gas flow by the sectional area (m2) of the conduit through which the sample gas flows.
Methods and apparatuses for measuring the concentration of a certain gas or the flow velocity of a sample gas, by using the above principle, on the basis of the propagation velocity or the propagation time of ultrasonic waves through the sample gas have been developed. For example, Japanese Unexamined Patent Publication (Kokai) No. 6-213877 describes an apparatus for measuring the concentration and the flow rate of a sample gas by measuring the propagation time of ultrasonic waves propagating between two ultrasonic transducers opposingly disposed in a conduit through which the sample gas flows. Further, Japanese Unexamined Patent Publications (Kokai) No. 7-209265 and No. 8-233718 describe an apparatus for measuring the concentration of a certain gas contained in a sample gas by measuring the propagation velocity or propagation time of ultrasonic waves propagating through a volume with a reflecting type apparatus including an ultrasonic transducer and an opposingly disposed reflector.
In such a method and an apparatus for measuring the concentration and the flow rate by using the propagation velocity of the ultrasonic waves, it is necessary to accurately measure the propagation time of the ultrasonic waves. However, the signal generated on the basis of the received ultrasonic waves always includes noise component, which makes difficult to determine the moment when ultrasonic waves are received by the ultrasonic transducer. Therefore, the propagation time of ultrasonic waves is indirectly estimated through a complex signal processing procedure or a complex hardware. For example, Japanese Unexamined Patent Publication (Kokai) No. 9-318644 describes a method for measuring a propagation time of ultrasonic waves in which the waveform of the received ultrasonic waves is integrated. After the results of the integration of the waveform reach a predetermined vale, the first zero-cross time instant is determined as the propagation time of the ultrasonic waves for the measurement of the flow rate. According to the method, the timing of the generation of the zero-cross signal is not fluctuated even if the amplitude of the received waves is fluctuated to some extent. Therefore, the obtained zero-cross time instant is relatively close to the moment when the ultrasonic waves actually reach. However, the obtained zero-cross time instant is not real propagation time of the ultrasonic waves. In particular, when the concentration is measured, the measurement error is strongly affected by the difference between the real propagation time and the zero-cross time instant.
Further, Japanese Unexamined Patent Publication (Kokai) No. 60-138422 describes a flow rate measuring device in which an envelope curve is calculated on the basis of the waveform of the received ultrasonic waves. The rise time of the envelope curve is calculated by an approximate equation to estimate the ultrasonic propagation time. However, a hardware is necessary to sample the received ultrasonic waves and a complex signal processing is necessary to calculate the envelope curve based on the sampled waveform. Therefore, according to the invention of JPP '422, it is difficult to provide a compact device with low cost.